TSTP Solution File: SET587^5 by Leo-III---1.7.12
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SET587^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 03:03:00 EDT 2024
% Result : Theorem 8.27s 2.82s
% Output : Refutation 8.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of formulae : 76 ( 7 unt; 8 typ; 0 def)
% Number of atoms : 279 ( 50 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 487 ( 121 ~; 99 |; 27 &; 227 @)
% ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 9 ( 9 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 81 ( 40 ^ 41 !; 0 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_type,type,
sk1: a > $o ).
thf(sk2_type,type,
sk2: a > $o ).
thf(sk3_type,type,
sk3: a ).
thf(sk4_type,type,
sk4: a ).
thf(sk5_type,type,
sk5: a > a ).
thf(sk6_type,type,
sk6: a ).
thf(sk8_type,type,
sk8: a ).
thf(1,conjecture,
! [A: a > $o,B: a > $o] :
( ( ( ^ [C: a] :
( ( A @ C )
& ~ ( B @ C ) ) )
= ( ^ [C: a] : $false ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cBOOL_PROP_45_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o] :
( ( ( ^ [C: a] :
( ( A @ C )
& ~ ( B @ C ) ) )
= ( ^ [C: a] : $false ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o] :
( ( ( ^ [C: a] :
( ( A @ C )
& ~ ( B @ C ) ) )
= ( ^ [C: a] : $false ) )
= ( ! [C: a] :
( ( A @ C )
=> ( B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
!= ( ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
!= ( ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) )
| ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(10,plain,
( ~ ( sk2 @ sk3 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(11,plain,
( ( sk1 @ sk3 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] : $false ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(31,plain,
( ( ( sk1 @ sk6 )
& ~ ( sk2 @ sk6 ) )
| ( sk1 @ sk3 ) ),
inference(func_ext,[status(esa)],[11]) ).
thf(35,plain,
( ( sk1 @ sk3 )
| ( sk1 @ sk6 ) ),
inference(cnf,[status(esa)],[31]) ).
thf(7,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(9,plain,
( ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) )
| ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(12,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) ) ),
inference(cnf,[status(esa)],[9]) ).
thf(50,plain,
! [A: a] :
( ( sk1 @ sk3 )
| ( sk2 @ A )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ( ( sk1 @ sk6 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[35,12]) ).
thf(51,plain,
( ( sk1 @ sk3 )
| ( sk2 @ sk6 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( sk6 ))]]) ).
thf(75,plain,
( ( sk1 @ sk3 )
| ( sk2 @ sk6 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,11]) ).
thf(76,plain,
( ( sk1 @ sk3 )
| ( sk2 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[75:[]]) ).
thf(34,plain,
( ( sk1 @ sk3 )
| ~ ( sk2 @ sk6 ) ),
inference(cnf,[status(esa)],[31]) ).
thf(92,plain,
( ( sk1 @ sk3 )
| ( ( sk2 @ sk6 )
!= ( sk2 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[76,34]) ).
thf(93,plain,
sk1 @ sk3,
inference(pattern_uni,[status(thm)],[92:[]]) ).
thf(24,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A )
| ~ ! [B: a] :
( ( sk1 @ B )
=> ( sk2 @ B ) )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) )
!= ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,5]) ).
thf(25,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A )
| ~ ! [B: a] :
( ( sk1 @ B )
=> ( sk2 @ B ) ) ),
inference(pattern_uni,[status(thm)],[24:[]]) ).
thf(29,plain,
! [A: a] :
( ~ ( sk2 @ ( sk5 @ A ) )
| ( sk2 @ A )
| ~ ( sk1 @ A ) ),
inference(cnf,[status(esa)],[25]) ).
thf(292,plain,
! [A: a] :
( ~ ( sk2 @ ( sk5 @ A ) )
| ( sk2 @ A )
| ( ( sk1 @ sk3 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[93,29]) ).
thf(293,plain,
( ~ ( sk2 @ ( sk5 @ sk3 ) )
| ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[292:[bind(A,$thf( sk3 ))]]) ).
thf(23,plain,
! [B: a,A: a] :
( ~ ( ( sk1 @ B )
& ~ ( sk2 @ B ) )
| ~ ( sk1 @ A )
| ( sk2 @ A ) ),
inference(func_ext,[status(esa)],[12]) ).
thf(28,plain,
! [B: a,A: a] :
( ( sk2 @ A )
| ~ ( sk1 @ A )
| ~ ( sk1 @ B )
| ( sk2 @ B ) ),
inference(cnf,[status(esa)],[23]) ).
thf(13,plain,
( ( ( sk1 @ sk4 )
& ~ ( sk2 @ sk4 ) )
| ~ ( sk2 @ sk3 ) ),
inference(func_ext,[status(esa)],[10]) ).
thf(14,plain,
( ~ ( sk2 @ sk3 )
| ~ ( sk2 @ sk4 ) ),
inference(cnf,[status(esa)],[13]) ).
thf(117,plain,
! [B: a,A: a] :
( ( sk2 @ A )
| ~ ( sk1 @ A )
| ~ ( sk1 @ B )
| ~ ( sk2 @ sk4 )
| ( ( sk2 @ B )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[28,14]) ).
thf(118,plain,
! [A: a] :
( ( sk2 @ A )
| ~ ( sk1 @ A )
| ~ ( sk1 @ sk3 )
| ~ ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[117:[bind(A,$thf( A )),bind(B,$thf( sk3 ))]]) ).
thf(208,plain,
! [A: a] :
( ( sk2 @ A )
| ~ ( sk1 @ A )
| ~ $true
| ~ ( sk2 @ sk4 ) ),
inference(rewrite,[status(thm)],[118,93]) ).
thf(209,plain,
! [A: a] :
( ( sk2 @ A )
| ~ ( sk1 @ A )
| ~ ( sk2 @ sk4 ) ),
inference(simp,[status(thm)],[208]) ).
thf(211,plain,
! [A: a] :
( ( sk2 @ A )
| ~ ( sk2 @ sk4 )
| ( ( sk1 @ sk3 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[93,209]) ).
thf(212,plain,
( ( sk2 @ sk3 )
| ~ ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[211:[bind(A,$thf( sk3 ))]]) ).
thf(183,plain,
! [A: a] :
( ( sk2 @ A )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) )
= ( ^ [B: a] : $false ) )
| ( ( sk1 @ sk3 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[93,12]) ).
thf(184,plain,
( ( sk2 @ sk3 )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
= ( ^ [A: a] : $false ) ) ),
inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( sk3 ))]]) ).
thf(190,plain,
( ( sk2 @ sk3 )
| ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) )
| ( ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) )
!= ( ^ [A: a] :
( ( sk1 @ A )
& ~ ( sk2 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[184,5]) ).
thf(191,plain,
( ( sk2 @ sk3 )
| ~ ! [A: a] :
( ( sk1 @ A )
=> ( sk2 @ A ) ) ),
inference(pattern_uni,[status(thm)],[190:[]]) ).
thf(200,plain,
( ( sk1 @ sk8 )
| ( sk2 @ sk3 ) ),
inference(cnf,[status(esa)],[191]) ).
thf(16,plain,
( ~ ( sk2 @ sk3 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk3 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[14]) ).
thf(18,plain,
( ~ ( sk2 @ sk3 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[16]) ).
thf(243,plain,
( ( sk1 @ sk8 )
| ( sk4 != sk3 )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[200,18]) ).
thf(244,plain,
( ( sk1 @ sk8 )
| ( sk4 != sk3 ) ),
inference(pattern_uni,[status(thm)],[243:[]]) ).
thf(17,plain,
( ~ ( sk2 @ sk3 )
| ( ( sk2 @ sk4 )
!= ( sk2 @ sk3 ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(26,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A )
| ~ ( sk2 @ sk3 )
| ( ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) )
!= ( ^ [B: a] :
( ( sk1 @ B )
& ~ ( sk2 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[12,10]) ).
thf(27,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ A )
| ~ ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[26:[]]) ).
thf(38,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ~ ( sk2 @ sk3 )
| ( ( sk2 @ A )
!= ( sk2 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[27,14]) ).
thf(39,plain,
( ~ ( sk1 @ sk4 )
| ~ ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( sk4 ))]]) ).
thf(15,plain,
( ~ ( sk2 @ sk3 )
| ( sk1 @ sk4 ) ),
inference(cnf,[status(esa)],[13]) ).
thf(249,plain,
( ( sk1 @ sk8 )
| ( sk1 @ sk4 )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[200,15]) ).
thf(250,plain,
( ( sk1 @ sk8 )
| ( sk1 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[249:[]]) ).
thf(341,plain,
( ( sk1 @ sk4 )
| ( ( sk1 @ sk8 )
!= ( sk1 @ sk4 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[250]) ).
thf(345,plain,
( ( sk1 @ sk4 )
| ( sk8 != sk4 ) ),
inference(simp,[status(thm)],[341]) ).
thf(30,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ A ) )
| ( sk2 @ A )
| ~ ( sk1 @ A ) ),
inference(cnf,[status(esa)],[25]) ).
thf(246,plain,
( ( sk1 @ sk8 )
| ~ ( sk2 @ sk4 )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[200,14]) ).
thf(247,plain,
( ( sk1 @ sk8 )
| ~ ( sk2 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[246:[]]) ).
thf(356,plain,
( ( sk8 != sk4 )
| ~ ( sk2 @ sk3 )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[345,39]) ).
thf(357,plain,
( ( sk8 != sk4 )
| ~ ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[356:[]]) ).
thf(422,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ A ) )
| ( sk2 @ A )
| ( ( sk1 @ sk3 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[93,30]) ).
thf(423,plain,
( ( sk1 @ ( sk5 @ sk3 ) )
| ( sk2 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[422:[bind(A,$thf( sk3 ))]]) ).
thf(240,plain,
( ( sk1 @ sk8 )
| ~ ( sk1 @ sk4 )
| ( ( sk2 @ sk3 )
!= ( sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[200,39]) ).
thf(241,plain,
( ( sk1 @ sk8 )
| ~ ( sk1 @ sk4 ) ),
inference(pattern_uni,[status(thm)],[240:[]]) ).
thf(199,plain,
( ~ ( sk2 @ sk8 )
| ( sk2 @ sk3 ) ),
inference(cnf,[status(esa)],[191]) ).
thf(358,plain,
( ( sk8 != sk4 )
| ( sk1 @ sk8 )
| ( ( sk1 @ sk4 )
!= ( sk1 @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[345,241]) ).
thf(359,plain,
( ( sk8 != sk4 )
| ( sk1 @ sk8 ) ),
inference(pattern_uni,[status(thm)],[358:[]]) ).
thf(580,plain,
$false,
inference(e,[status(thm)],[10,293,28,212,244,17,12,39,345,209,18,250,30,5,247,14,184,357,93,29,423,27,3,241,199,359,15,200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SET587^5 : TPTP v8.2.0. Released v4.0.0.
% 0.10/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Mon May 20 13:01:39 EDT 2024
% 0.14/0.35 % CPUTime :
% 0.82/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.08/0.98 % [INFO] Parsing done (115ms).
% 1.08/0.98 % [INFO] Running in sequential loop mode.
% 1.62/1.24 % [INFO] eprover registered as external prover.
% 1.62/1.24 % [INFO] cvc4 registered as external prover.
% 1.62/1.25 % [INFO] Scanning for conjecture ...
% 1.75/1.32 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.75/1.34 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.75/1.34 % [INFO] Problem is higher-order (TPTP THF).
% 1.75/1.34 % [INFO] Type checking passed.
% 1.75/1.34 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 8.27/2.82 % External prover 'e' found a proof!
% 8.27/2.82 % [INFO] Killing All external provers ...
% 8.27/2.82 % Time passed: 2320ms (effective reasoning time: 1834ms)
% 8.27/2.82 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 8.27/2.82 % Axioms used in derivation (0):
% 8.27/2.82 % No. of inferences in proof: 68
% 8.27/2.82 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2320 ms resp. 1834 ms w/o parsing
% 8.27/2.86 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.27/2.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------